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➗ Math · Numbers and Algebra · Lesson 2 of 8 · 6 min

Adding, subtracting, multiplying and dividing fractions and decimals

🍰 Recipes, shift hours and tablet counts all come in halves and quarters. Get the four operations right and a whole class of TEAS items becomes free points.

💡 Key idea

Common denominator to add or subtract; straight across to multiply; flip the second fraction to divide.

🧠 The idea

To ADD or SUBTRACT fractions, rewrite them with a COMMON DENOMINATOR first, then combine only the numerators: 1/3 + 1/4 = 4/12 + 3/12 = 7/12. Never add the denominators. To MULTIPLY fractions, multiply straight across: 2/3 × 3/5 = 6/15 = 2/5. To DIVIDE, keep the first fraction, flip the second (its RECIPROCAL) and multiply: 3/4 ÷ 1/2 = 3/4 × 2/1 = 6/4 = 1 1/2. Change mixed numbers to improper fractions before multiplying or dividing: 2 1/2 = 5/2. With decimals, line up the decimal points to add or subtract. To multiply decimals, multiply as whole numbers, then count the total decimal places in both factors: 0.4 × 0.3 = 0.12. To divide by a decimal, move the point in both numbers until the divisor is a whole number: 1.2 ÷ 0.3 = 12 ÷ 3 = 4.

✏️ Worked example

A nurse works 3 3/4 hours before lunch and 4 1/2 hours after. How many hours is that in all?
Step 1: Add the whole numbers: 3 + 4 = 7.
Step 2: Common denominator for the fractions: 3/4 + 1/2 = 3/4 + 2/4 = 5/4.
Step 3: Rewrite 5/4 as 1 1/4.
Step 4: Combine: 7 + 1 1/4 = 8 1/4.
Answer: 8 1/4 hours (8.25 hours).

📌 Takeaways

  • Add/subtract: common denominator, combine numerators only.
  • Divide: keep, change to multiply, flip the second fraction.
  • Decimal products: count decimal places in both factors.

✅ Check yourself

Question 1 of 3

What is 2/5 + 1/3?

  1. 3/15
  2. 2/15
  3. 3/8
  4. 11/15
Show the answer and rationale

Answer: D

The common denominator is 15: 2/5 = 6/15 and 1/3 = 5/15, so the sum is 11/15. The answer 3/8 adds the tops and the bottoms separately, a classic mistake; 2/15 multiplies instead of adding.

Question 2 of 3

What is 2/3 ÷ 4/9?

  1. 3/2
  2. 8/27
  3. 2/9
  4. 2/3
Show the answer and rationale

Answer: A

Flip the second fraction and multiply: 2/3 × 9/4 = 18/12 = 3/2 (that is 1 1/2).The answer 8/27 multiplies without flipping, 2/9 subtracts the fractions instead of dividing, and 2/3 just repeats the first fraction.

Question 3 of 3

What is 0.6 × 0.05?

  1. 0.3
  2. 3.0
  3. 0.003
  4. 0.03
Show the answer and rationale

Answer: D

Multiply 6 × 5 = 30, then count decimal places: one in 0.6 and two in 0.05, three in all, so 30 becomes 0.030 = 0.03. The answer 0.3 counts only two places, and 0.003 counts four.

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